
and \(\odot \)  represents element-wise multiplication (i.e. the Hadamard product).
Note that a similar optimization arises in the computation of the amplitudes of DMD modes [1]}.
While mathematically correct, numerical implementations of (REF )
can be difficult. Specifically, issues arise because the Gramian matrix \({\mathcal {X}} {\mathcal {X}}^\ast \)  will typically be large and ill-conditioned.
Thus, we expect that one could find more efficient algorithms to calculate \(A\) ,
possibly by adapting methods for fast solutions of Toeplitz systems
[2]}, [3]}, [4]}.
